At present, you can't move the square. But we hear you, and would like to make that a feature in the future! For now, however, the Enhanced Recording features gives you much more flexibility.

With Enhanced Recording, Blue Jeans records shared content and participant video as separate streams. You can then download both of the MP4 files and make a composite video with an editor like Camtasia. If you've ever seen a video where the picture-in-picture moves around, or with effects like zooming in and out, then it was produced in a similar way: someone imported two or more video files and then exported a new composited MP4 file.